Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample1.3s (40.1%)

Results

1.2s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 62 to 47 computations (24.2% saved)

simplify44.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1024×	`fma-neg_binary64`
476×	`rules-6_binary64`
463×	`rules-20_binary64`
252×	`rules-5_binary64`
250×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	34	29
2	90	29
3	313	29
4	1329	29
5	3691	27
6	4874	27

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (sqrt.f64 (fma.f64 (.f64 v v) -3 1)) (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))))

Compiler

Compiled 76 to 55 computations (27.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 (*.f64 v v) -3 1))
✓	0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v)))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 (.f64 v v) -3 1)) (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))))

series19.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

10.0ms	(.f64 (sqrt.f64 (fma.f64 (.f64 v v) -3 1)) (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))))
5.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v)))
4.0ms	(sqrt.f64 (fma.f64 (*.f64 v v) -3 1))

rewrite168.0ms (5.3%)

Algorithm

2×	batch-egg-rewrite

Rules

551×	`prod-diff_binary64`
292×	`egg-rr`
226×	`log1p-udef_binary64`
131×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`

Counts

3 → 292

Calls

3 calls:

158.0ms	(sqrt.f64 (fma.f64 (*.f64 v v) -3 1))
158.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v)))
158.0ms	(.f64 (sqrt.f64 (fma.f64 (.f64 v v) -3 1)) (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	329	52
2	3686	52
3	5049	52
0	0	0
1	0	0

simplify37.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

110×	`fma-def_binary64`
97×	`rules-20_binary64`
82×	`rules-13_binary64`
68×	`rules-11_binary64`
48×	`rules-7-rev_binary64`

Counts

328 → 339

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	1093
1	362	1093
2	1646	1093

prune377.0ms (11.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	338	2	340

Error

Counts

340 → 2

Alt Table

Status	Error	Program
	0.0b	(/.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))) (/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))
▶	0.0b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))

Compiler

Compiled 14452 to 10792 computations (25.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.2b	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
✓	0.2b	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

series18.0ms (0.6%)

Counts

3 → 3

Calls

3 calls:

8.0ms	(*.f64 (pow.f64 v 2) (sqrt.f64 2))
5.0ms	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
4.0ms	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))

rewrite87.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

914×	`fma-neg_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
195×	`egg-rr`
165×	`log-pow_binary64`

Counts

3 → 195

Calls

3 calls:

83.0ms	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
83.0ms	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
83.0ms	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	275	36
2	3298	36
3	4825	36
0	0	0
1	0	0

simplify117.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1159×	`fma-neg_binary64`
523×	`rules-33_binary64`
486×	`rules-20_binary64`
371×	`rules-5-rev_binary64`
328×	`rules-24-rev_binary64`

Counts

198 → 198

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	18	30
2	31	30
3	47	30
4	72	30
5	119	30
6	242	30
7	682	30
8	2003	30
9	4219	8
10	4777	8
11	4980	8
12	4590	8

prune214.0ms (6.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	198	2	200

Error

Counts

200 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))) (/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))
✓	0.0b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))

Compiler

Compiled 4253 to 3317 computations (22% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fma.f64 (*.f64 v v) -3 1))
✓	0.0b	(/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1)))
	0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v)))
✓	0.0b	(/.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))) (/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))

series17.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(/.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))) (/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))
5.0ms	(/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1)))

rewrite83.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
141×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`
136×	`add-log-exp_binary64`

Counts

2 → 98

Calls

2 calls:

80.0ms	(/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1)))
80.0ms	(/.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))) (/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	351	38
2	3951	38
3	4955	38
0	0	0
1	0	0

simplify30.0ms (1%)

Algorithm

1×	egg-herbie

Rules

148×	`fma-def_binary64`
108×	`rules-13_binary64`
94×	`rules-20_binary64`
69×	`rules-21_binary64`
64×	`rules-14-rev_binary64`

Counts

122 → 141

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	128	1029
1	435	1029
2	1944	1029

prune389.0ms (12.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	375	0	375
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	375	2	377

Error

Counts

377 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (-.f64 1 (.f64 v v))) (/.f64 1 (sqrt.f64 (fma.f64 (*.f64 v v) -3 1))))
✓	0.0b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))

Compiler

Compiled 14807 to 11257 computations (24% saved)

regimes195.0ms (6.2%)

Accuracy

Total 0.0b remaining (10.2%)

Threshold costs 0.0b (10.2%)

Counts

53 → 1

Compiler

Compiled 3060 to 2393 computations (21.8% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	17	29
2	16	29

end57.0ms (1.8%)

Compiler: Compiled 75 to 59 computations (21.3% saved)

Details

analyze6.0ms (0.2%)

sample1.3s (40.1%)

simplify44.0ms (1.4%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series19.0ms (0.6%)

rewrite168.0ms (5.3%)

simplify37.0ms (1.2%)

prune377.0ms (11.9%)

localize7.0ms (0.2%)

series18.0ms (0.6%)

rewrite87.0ms (2.8%)

simplify117.0ms (3.7%)

prune214.0ms (6.8%)

localize12.0ms (0.4%)

series17.0ms (0.5%)

rewrite83.0ms (2.6%)

simplify30.0ms (1%)

prune389.0ms (12.3%)

regimes195.0ms (6.2%)

simplify1.0ms (0%)

end57.0ms (1.8%)

Profiling